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2 years ago

11

A____ is a fixed position in space and has no dimensions or size. hins

2 answers:

Nitella [24]2 years ago

8 0

Answer:

A <u>point</u> is a fixed position in space and has no dimensions or size.

amid [387]2 years ago

6 0

Answer:

Point

Step-by-step explanation:

This is the definition of a point.

A "point" is a fixed position in space and has no dimensions or size.

Cheers.

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What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot

Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

$a = 500$ --- starting balance

$m = 10$ --- monthly rate

Her brother

$a = 100$ ---- starting balance

$r = 10\%$ --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

$y = ab^x$

Where $b = 1 + r$

So, we have:

$y = ab^x$

$y = 100 *(1 + 10\%) ^x$

$y = 100 *(1 + 0.10) ^x$

$y = 100 *(1.10) ^x$

Hence:

$g(x) = 100 *(1.10) ^x$

Next, we calculate Molly's function (a linear function)

The monthly function is:

$y = mx + a$

So, we have:

$y = 10x + 500$

Annually, the function will be:

$y = 10x*12 + 500$

$y = 120x + 500$

So, we have:

$f(x) = 120x + 500$

At this point, we have:

$f(x) = 120x + 500$ ---- Molly

$g(x) = 100 *(1.10) ^x$ ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

$y = 120x + 500$

The slope of a linear function with the form: $y = mx + b$ is m

By comparison:

$m = 120$

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

$m = 120$

For his brother:

Rate of change is calculated using:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(40) - g(32)}{40 - 32}$

$m = \frac{g(40) - g(32)}{8}$

Calculate g(40) and g(32)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{40} =4526$

$g(32) = 100 * 1.10^{32} = 2111$

So, we have:

$m = \frac{4526 - 2111}{8}$

$m = \frac{2415}{8}$

$m = 302$

By comparison: $302 > 120$

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(30) - g(24)}{30 - 24}$

$m = \frac{g(30) - g(24)}{6}$

Calculate g(30) and g(24)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{30} =1745$

$g(32) = 100 * 1.10^{24} = 985$

So, we have:

$m = \frac{g(30) - g(24)}{6}$

$m = \frac{1745 - 985}{6}$

$m = \frac{760}{6}$

$m = 127$

By comparison: $127 > 120$

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(4) - g(0)}{4 - 0}$

$m = \frac{g(4) - g(0)}{4}$

Calculate g(4) and g(0)

$g(x) = 100 *(1.10) ^x$

$g(4) = 100 * 1.10^4 =146$

$g(0) = 100 * 1.10^{0} = 100$

So, we have:

$m = \frac{g(4) - g(0)}{4}$

$m = \frac{146 - 100}{4}$

$m = \frac{46}{4}$

$m = 11.5$

By comparison: $120>11.5$

Hence, Molly's account has a faster rate over [0,4]

(c) is false

4 0

2 years ago

Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed?

kykrilka [37]

we will select each options and find zeros

(a)

$g(x)=x^2-4x-21$

for finding x-intercept , we can set g(x)=0

and then we can solve for x

$g(x)=x^2-4x-21=0$

now, we can factor it

$(x-7)(x+3)=0$

we get

$x=7,x=-3$

so, this is TRUE

(b)

$g(x)=(x-3)(x+7)$

we can set it to 0

and then we can solve for x

$g(x)=(x-3)(x+7)=0$

we get

$x=3,x=-7$

so, this is FALSE

(c)

$g(x)=3x^2-12x-63$

we can set it to 0

and then we can solve for x

$g(x)=3x^2-12x-63 =0$

$3(x^2-4x-21) =0$

$3(x-7)(x+3) =0$

$x=-3,x=7$

so, this is TRUE

(d)

$g(x)=-(x+3)(x-7)$

now, we can set it to 0

and then we can solve for x

$g(x)=-(x+3)(x-7)=0$

$x=-3,x=7$

so, this is TRUE

(e)

we have

$g(x)=x^2+4x-21$

now, we can set it to 0

and then we can solve for x

$g(x)=x^2+4x-21=0$

$(x+7)(x-3)=0$

$x=-7,x=3$

so, this is FALSE

5 0

2 years ago

Read 2 more answers

Order of fractions from least to greatest 5/8,3/4,1/2,9/16

rusak2 [61]

Answer:

1/2, 9/16, 5/8, 3/4

Step-by-step explanation:

3 0

2 years ago

3 1183 long division

Triss [41]

= 394 R 1

= 394 1/3

1183 divided by 3 equals
394 with a remainder of 1

3 0

2 years ago

I bet you 10 points you will not answer this<br><br> I think its B i need assurance

Flauer [41]

Answer:

(a) seems to be the closest to being correct of these five statements.

Step-by-step explanation:

Let's go through the list of possible descriptors:

a) There are no outliers. This seems to be the response most likely to be correct.

b) The distribution is not skewed left. It's skewed right.

c) The center is not 44. From what I see, the center is 48.

d) This distribution is not bimodal; it does not have two peaks.

d) The spread is not 38 to 67; it's 29 to 67.

5 0

2 years ago